Linked from

The 48 pages that link to Permutation, each with the reason it gives.

• Binomial coefficientCompared with: Unlike a binomial coefficient, permutations distinguish different orders of the same selection.

• DeterminantNarrower topic: The determinant's defining sum assigns a sign and product to each permutation.

• CombinatoricsBroader topic: Permutations count arrangements in which changing the order creates a different outcome.

• SequenceCompared with: A permutation is a sequence constrained to contain each chosen element once.

• Group actionRelated: Each group element acts as a permutation of the underlying set.

• FactorialRelated: The n! permutations of n distinct objects count every possible ordering.

• GroupRelated: Permutations compose associatively, have an identity, and can be undone.

• BijectionBroader topic: Permutations are bijections whose domain and codomain are the same set.

• Fermat's little theoremRelated: Multiplication by a permutes the nonzero residues modulo p, yielding a product-based proof.

• Permutation groupNarrower topic: Each element of a permutation group is a permutation of the underlying set.

• Symmetric groupBroader topic: Each element of a symmetric group is a permutation.

• Orbit-stabilizer theoremRelated: Each group element acts as a permutation of the set.

• Rule of productBroader topic: Choosing successive positions without replacement gives the product used to count permutations.

• CombinationCompared with: It is the order-sensitive counterpart to an ordinary combination.

• Permutation matrixNarrower topic: The locations of the matrix’s 1s encode a permutation of row or column indices.

• Rearrangement inequalityNarrower topic: The inequality compares product sums across permutations of one sequence.

• Sorting algorithmRelated: A correct sort changes element order without losing or duplicating elements.

• Stars and barsCompared with: Stars and bars encodes allocations without treating identical objects as distinct.

• Falling factorialRelated: The falling factorial counts ordered selections of n distinct objects from x choices.

• MajorizationRelated: Majorization ignores the original order of entries by sorting or permuting vectors.

• Multinomial coefficientNarrower topic: A multinomial coefficient counts permutations after arrangements within groups are treated as indistinguishable.

• PlugboardNarrower topic: On cipher machines, plugboard wiring implements a permutation of symbols.

• Standard 52-card deckNarrower topic: Every possible deck order is a permutation of its 52 distinct cards.

• AnagramNarrower topic: An anagram rearranges a word’s letters, making it a permutation constrained by letter identity.

• Latin squareNarrower topic: Each row and column can be viewed as a permutation of the symbols.

• Sol LeWittRelated: Permutation systems generate many distinct arrangements from a limited set of forms.

• Wilson's theoremRelated: Multiplication by a nonzero residue permutes the nonzero residues modulo a prime.

• Dilworth's theoremRelated: Order comparisons among permutation entries yield chain and antichain decompositions.

• Laplace expansionNarrower topic: Permutation signs explain the alternating signs in determinant terms.

• Riemann series theoremRelated: A rearrangement must reorder every term without omitting or duplicating any.

• Block cipherRelated: For a fixed key, a block cipher maps every possible input block to a unique output block.

• Discrete uniform distributionRelated: Uniform sampling over permutations models a randomly chosen ordering of finite outcomes.

• Erdős–Szekeres theorem (monotone subsequences)Narrower topic: Relabeling the distinct values by rank reduces the theorem to a statement about permutations.

• Binet–Cauchy identityRelated: Determinants encode signs of permutations, which govern signs in minor expansions.

• Cauchy–Binet formulaRelated: Determinant expansions over permutations underlie the formula's signs and terms.

• Georges PerecRelated: Permutations and combinatorial structures informed Perec’s methods for generating literary forms.

• Muirhead's inequalityRelated: The symmetric sum is formed by permuting the exponents among the variables.

• Sliding puzzleNarrower topic: Every tile arrangement can be represented as an ordering of the tiles and vacancy.

• Travelling salesman problemRelated: Candidate tours can be represented as city orderings, though many orderings describe the same cycle.

• Bertrand's ballot theoremRelated: A random ballot is a permutation of the votes, with votes of the same candidate treated as indistinguishable.

• Leibniz formula for determinantsNarrower topic: Each term chooses columns through one permutation of the matrix’s rows.

• Mutually orthogonal Latin squaresRelated: Every row and column of a Latin square is a permutation of its symbols.

• Algebraic combinatoricsRelated: Permutations are fundamental objects studied through algebra, statistics, and enumeration.

• Combinatorial principlesRelated: The product rule counts the successive positions in an arrangement.

• Lah numberRelated: Concatenating the lists gives a permutation, with cuts marking the blocks.

• Lévy–Steinitz theoremRelated: Rearranging a series means applying a permutation to its term indices.

• Partial permutationCompared with: Unlike a full permutation, a partial permutation need not use every element.

• War (card game)Narrower topic: A shuffled deck is one ordering of its cards, and War’s outcomes depend on that order.